need some help setting up a few problems

Here are the problems I am having difficulty with:

1. Given the characteristic equation of a 4th order differential equation has repeated roots of i and - i,
a) write the general solution of the differential equation
b)write the original differential equation

2.
a) write the general solution near x = 0.
b) find the indicial equation and the exponents at the singularity.

Those are the 2 problems I am having trouble with. Its all just on how to start.. Here is what im am doing for each of them:

1.[/B]
A. I dont know how to do....
B.

2. With this you can just substitute
where n = 0 to infinity and its appropriate derivatives. correct?

1.Given the characteristic equation of a 4th order differential equation has repeated roots of i and - i,
a) write the general solution of the differential equation
b)write the original differential equation

If are roots of the characteristic equation with multiplicity 2, choose